In DNA dynamic nanotechnology, a toehold-mediated DNA Strand-displacement reaction has demonstrated its capability in building complex autonomous system. In most cases, the reaction is performed in pure DNA solution that is essentially a one-phase system. In the present work, we systematically investigated the reaction in a heterogeneous media, in which the strand that implements a displacing action is conjugated on gold nanoparticles. By monitoring the kinetics of spherical nucleic acid (SNA) assembly driven by toehold-mediated strand displacement reaction, we observed significant differences, i.e., the abrupt jump in behavior of an "off/on switch", in the reaction rate when the invading toehold was extended to eight bases from seven bases. These phenomena are attributed to the effect of steric hindrance arising from the high density of invading strand conjugated to AuNPs. Based on these studies, an INHIBIT logic gate presenting good selectivity was developed.